$Factorise: (2 l + m)^{2} - 8 l m$

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Solution

$Given: (2 l + m)^{2} - 8 l m$

$On expanding (2 l + m)^{2} using the identity (a + b)^{2} = a^{2} + 2 a b + b^{2}, we get,$
$(2 l + m)^{2} = (2 l)^{2} + 4 l m + m^{2}$

$So, (2 l + m)^{2} - 8 l m = (2 l)^{2} + 4 l m + m^{2} - 8 l m = (2 l)^{2} + (- 4 l m) + m^{2}$

$By comparing this with the same identity (a + b)^{2} = a^{2} + 2 a b + b^{2}, a = 2 l, b = - m (2 l + m)^{2} - 8 l m = (2 l - m)^{2}$

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